1. Field of the Invention
The present invention relates to a displacement transducer. More particularly, the invention relates to a displacement transducer comprising a strain gage mounted to a curved arc of flexible material.
2. Description of Related Art
Strain gages are well known for measuring relative displacement in specimens. A typical strain gage is a variable resistance strain sensing element affixed to a strip of flexible backing material. Most commonly, the sensing element is an electrical conductor pathway arranged in an accordion pattern as known in the art. The strain gage is mounted to a specimen surface to measure displacement in the specimen.
A positive displacement in the specimen (i.e. an expansion) causes the gage to stretch. As a result, the electrical conductor pathway is also stretched which causes the diameter of the pathway to narrow. Because electrical resistance is inversely proportional to the diameter of the electrical pathway, this narrowing increases the resistance of the pathway as the gage is stretched. Positive displacement is measured by correlating the difference in potential (xcex94V) resulting from the change in resistance (positive xcex94R) to the magnitude of stretching.
Conversely, compression of the gage due to a negative displacement (i.e. compression of the specimen) increases the electrical pathway""s diameter thus lowering its resistance. This reduction in electrical resistance (negative xcex94R) results in a negative change of potential which is correlated to the magnitude of the compression.
Further aspects and details of strain gage technology are set forth in the following references, the contents of which are incorporated herein by reference: A Method for Recording Tendon Strain in Sheep During Locomotion, Kear M., Smith R. N., Acta Orthop Scand, 46: 896-905, 1975; Theoretical Analysis of an Implantable Force Transducer (IFT) for Tendon and Ligament Structures, Xu W. S., Butler D. L., Stouffer D. C., Grood E. S., Glos D. L., Transactions of the ASME Journal of Biomechanical Engineering, 114: 170-177, 1992; In Situ Calibration of Miniature Sensors Implanted into the Anterior Cruciate Ligament Part I: Strain Measurements, Markolf K. L., Willems M. J., Jackson S. R. and Finerman G. A. M., Journal of Orthopaedic Research, 16:455-563, 1998; Anterior Cruciate Ligament Strain In-Vivo: A Review of Previous Work, Beynnon B. D., Fleming B. C., Journal of Biomechanics, 31: 519-525, 1998; A Note on the Application and Evaluation of the Buckle Transducer for Knee Ligament Force Measurement, Lewis J. L., Lew W. D., Schmidt J., Transactions of the ASME Biomechanical Engineering, 104: 125-128, 1982; Design and Performance of a Modified Buckle Transducer for Measurement of Ligament Tension, Barry D., Ahmed A. M., Transactions of the ASME Journal of Biomechanical Engineering, 108: 149-152, 1986; and Buckle Muscle Tension Transducer: What Does It Measure?, Hahs D. W., Stiles R. N., Journal of Biomechanics, 22:2, 165-166, 1989.
Existing strain gages perform adequately for measuring displacements on the order of 0.5-5% of the gage length. Beyond this range, non-linearities, noise and damage to the gage elements may occur. For a 5 mm strain gage, this range would be 25-250 xcexcm. Gages for measuring very small displacements, on the order of 5 xcexcm, suffer from several drawbacks. First, such strain gages are very small, perhaps 2 or 3 mm in length, and can often only measure displacements up to 5% or even 1% of their length without being damaged. For example, a 3 mm gage may only be able to measure a displacement of about 30 xcexcm without damage. This is because the electrical conductor pathways have exceedingly small diameter (i.e. on the order of 1 xcexcm) which are easily snapped if stretched beyond their mechanical limits.
Second, the xcex94R for very small displacements is also very small. Hence, even a 3 mm gage with an upper displacement limit of 30 xcexcm may have a resolution of only 5-10 xcexcm (or 18-33% of scale), making accurate measurement in this range difficult to achieve. Resolution can be improved somewhat with electronic signal amplification and conditioning. However, these methods amplify noise as well as signal, and only marginal success has been achieved at measuring very small displacements.
Third, such small strain gages quickly experience nonlinear or exponential xcex94R for very small displacements. Exponential xcex94R will result in exponential xcex94V output. Nonlinear or exponential output complicates gage calibration and further obscures accurate measurement of displacement.
There is a need in the art for a strain or displacement transducer that can measure very small displacements without suffering from the above shortcomings. Preferably, such a transducer will have very high resolution (down to 1 xcexcm or better) at displacements of less than 100 xcexcm, preferably less than 50 xcexcm, will be able to measure displacements greater than 5% or even 10% of the strain gage length, and will have a substantially linear xcex94R in that range.
A displacement transducer is provided having a substrate having a bridge and a strain gage securely mounted to the bridge. The strain gage is mounted to the bridge in a pre-stressed condition.
A displacement transducer is also provided having a substrate having a bridge and a strain gage securely mounted to the bridge, wherein the bridge is a polyfaceted arc.
A hoop strain device for measuring radial expansion of a femur or other bone is also provided. The hoop strain device comprises a flexible band and a displacement transducer. The flexible band is adapted to surround and be in intimate contact with a bone circumference. The displacement transducer is mounted on the flexible band, and comprises a substrate having a curved arc and a strain gage securely mounted to the curved arc.